Question

If a solid sphere of mass $5 \,kg$ and a disc of mass $4 \,$ have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$. The the value of $x$ is ___

Answer 1

$I _1=\frac{2}{5} m _1 R ^2+ m _1 R ^2 $
$I _1= m _1 R ^2\left(\frac{7}{5}\right) $
$ I _1=7 R ^2$

$ I _2=\frac{ m _2 R ^2}{4}+ m _2 R ^2 $
$ I _2=\frac{5}{4} m _2 R ^2 $
$ I _2=5 R ^2 $
$\frac{ I _2}{ I _1}=\frac{5}{7} $
$ x =5$